On the multiplication operators and multipliers on weighted spaces of holomorphic functions on the upper halfplane

Abstract

In this paper‎, ‎we find necessary and sufficient conditions such that under these conditions a self map multiplication operator between weighted spaces of holomorphic functions is ‎‎Fredholm or closed range operator‎. ‎We also obtain a characterization of multipliers for certian type of weights operators between weighted spaces of holomorphic functions on the upper halfplane. ‎Our results will remain valid for any simply connected domain in the complex plane instead of the upper halfplane ‎.